Closely related work. We generalize the problem of blind demixing to graph filters and signals, providing both algorithms and theoretical analysis. Relative to [1]}, which deals with the blind deconvolution of a single graph signal (diffused by a single graph filter), the demixing setup considered here deals with multiple graph signals (each associated with its own graph filter and own graph) with the goal of separating them from a mixture.
On top of considering different operating conditions, demixing is intrinsically more challenging since it is a more severely undetermined problem.
Recently, a data-driven deep learning approach was proposed for the demixing of non-linear network processes [2]}.
Though relevant in practice, the approach in [2]} requires access to training data and, more importantly, lacks an in-depth theoretical analysis as the one presented here.
Finally, relative to the classical (non-graph) demixing setup in [4]}, the approach in our paper not only can be used in applications dealing with networks and irregular information domains, but also entails different technical modeling assumptions, namely: (1) sparsity of the input signals; (2) generalization of random Fourier matrices (in the classical setup) to random unitary matrices (in the GSP setup); and (3) consideration of multiple signal supports (one per signal).
